In mammalian species, primarily in rodents, primates and canids, social monogamy is found in only 3-5% species and genetic monogamy appears to be rare. There is compelling evidence that the beavers (genus Castor) are a monogamous species. In this study we examined the genetic mating system of social monogamous Eurasian beaver (Castor fiber) and tested for extra-pair copulation (EPC) in a free-ranging population in Norway. In this region beavers have been captured and monitored since 1998. We used 30 Single Nucleotide Polymorphism (SNPs) to test for EPC in 100 beavers (44 offspring and 56 dominant individual of beavers in 10 family groups). For all the 100 samples all putative parents were known. Of the 30 SNPs used in this study we got reliable results for 27. We did not find any evidence for EPC in this population. Based on the genetic data it appears that the Eurasian beaver is a strict genetically monogamous species. These results are in concordance with the observational data. This is the first genetic study on EPC in Eurasian beavers by using SNPs.